Kinematics: Chapter 4, X Physics

MECHANICS:

The branch of physics which deals with the objects which are in state of rest or in a

state of motion is called mechanics.

Kinematics:

The branch of physics which deals with the description of motion of object without

reference to the force or agent causing motion is called kinematics.

Rest:

If a body does not change its position with respect to its surrounding than it is said to

be in a state of rest.

OR

If co-ordinates of position of object remains same than it is said to be in state of rest..

Example:

A box placed at one corner

A bus standing at the bus stop

Motion:

If a body changes its position with respect to its surrounding than it is said to be in a

state of motion.

OR

If the co-ordinates representing the position of an object changes tune to time that it is

said to be in a state of motion.

Eg: Motion of train on plateform

Motion of car on street

Kinds of motion:

(1) Transistory motion / Linear motion:

A motion of a body in which every particle of the object is being displaced by

the same amount is called translational motion.

OR

If an object moves in a straight line than if is said to be in a state linear motion.

Eg: Motion of falling body

Motion of car on road

(2) Rotational motion / Circular motion:

When an object spins or rotates about a fixed point or axis, its motion is called

rotation motion.

OR

The motion of body in a circular orbit is called circular or rotational motion.

Eg: Motion of electric fan

Motion of planet around the sun

(3) Oscillatory Motion / Vibratory Motion:

When a pendulum swings from one side to other side and back motion is said to

os cillatory or viberatory motion.

OR

To and from motion abot the mean position is called viberatory or oscillatory

motion.

Eg: Motion of simple pendulum

Motion of stretched string

(4) Projectile Motion:

Motion of an object in a curve path is called projectile motion.

OR

When an object moves in a parabolic path and falls under the action of gravity

than its motion is said to be projectile motion.

Eg: Motion of projectile

A ball thrown horizontally with certain angle.

Distance:

Gap or space covered by a body between two points in any direction is called distance.

Units: M.K.S. system ----- meter ---------- m

C.G.S system ----- centimeter---------- c

F.P.S system ------ foot ---------- ft

Displacement:

Minimum shortest distance covered by a body between two points in a straight line in

a direction of one another is called displacement. It is denoted by S.

OR

Least possible distance between points in the direction of one another is called

displacement.

Displacement must be in straight line i.e. unidirectional.

It is denoted by S.

Units: M.K.S. System Meter m

C.G.S. System Centimetre cm

F.P.S. System Foot ft

Figure:

Distance

Displacement

Speed:

“Rate of covering distance is called speed.”

OR

“Distance covered by a body in a unit time (one second) is called speed.”

OR

“The ratio of distance with respect to time is called speed.”

Average Speed:

“The ratio of total distance covered by a body to the total time required to cover it is

called average speed.”

OR

“The average speed is determined by the amount of distance traveled by the body in

the given time duration.”

Mathematically, Average Speed = Total Distance Covered

Total time covered

Symbolically V = S

t

Units: M.K.S. System m/s meter / second

C.G.S. System cm/s centimeter / second

F.P.S. System ft/s Foot / second

Velocity:

“Speed of a body in a specified direction is called velocity.”

OR

“Rate of change of displacement is called velocity.”

OR

“Distance covered by a body in a unit time (one second) in a particular

direction is called velocity.”

Average Velocity:

“The ratio of total displacement covered by the body to the total time require to cover

it is called average velocity.”

OR

“The average velocity of a moving is given by the displacement divided by the time

elapsed.”

Mathematically, average velocity = Total displacement

Total time

Symbolically V_2x = S

t

Units: M.K.S. System m/s meter / second

C.G.S. System cm/s centimeter / second

F.P.S. System ft /s Foot / second.

Uniform Velocity:

“If the velocity remains same at the different interval in equal interval of time than it is

said to be specified velocity.”

OR

“The velocity of the body is said to be uniform if it covers equal distance in equal

interval of time in specified direction.”

Variable Velocity:

“If the velocity change at the different intervals of time than it is said to be variable

velocity.”

OR

“The velocity of the body is said to be variable if it do not equal distance in equal

intervals of time in specified direction.”

Acceleration:

“Rate of change of velocity is called acceleration.”

OR

“Change of velocity in a unit time (one second) is called acceleration.”

OR

“The ratio of change in velocity to the time requires to produce that changes is called

acceleration.”

Acceleration is denoted by symbol a. It is taken positive when velocity is increasing and

negative when velocity is decreasing.

Acceleration can be calculated with the following mathematical equation.

Acceleration = Change in velocity

Time interval

a = DV

DT

a = Vf Vi

Dt

Hence a is the acceleration, V_i is the interval velocity, V_f is the final velocity and ∆t is the

time interval.

Units: M.K.S. System m/s² meter / second

C.G.S System cm/s² Centimetre / second

F.P.S. System ft / s² Foot / second

Average Acceleration:

“The ratio between total change in velocity and the time require to produce that

change is called Average Acceleration.”

Mathematically, Acceleration = Change in velocity

Time

aav = DV

Dt

Uniform Acceleration:

“If the velocity of a body moving along a straight line changes uniform in equal

intervals of time, however short the interval may be, the acceleration so produced is

called uniform acceleration.”

OR

“If acceleration remains same at the different interval of time than it is called uniform

acceleration.”

Positive Acceleration:

“If the speed is increasing than acceleration is called positive acceleration.”

Its direction is in the direction of motion.”

Negative Acceleration:

“If the speed is decreasing than acceleration is negative and is called negative

acceleration.” It is also called deceleration or retaration.

Equations Of Uniformly Acceleration Rectilinear Motion:

The are three basic equations concenting acceleration, velocity, distance, in case of

uniformly accelerated rectilinear motion.

First Motion:

Let a body starts its motion with velocity “V_i”. Let after time “ t “ its velocity becomes

“V_f “. During such duration it covered distance with uniform acceleration “ a “.

By definition, acceleration is given as

Acceleration = Change in velocity

Time

OR av = DV __________________(1)

t

Where, DV is the change in velocity given as

DV = V_f – V_i _________________(2)

Substituting (2) in (1)

a = V_f – V_i /Vt

at = V_{f -} V_i

V_i + at = V_f

OR

V_{f =} V_i + at

Which is called first equation of motion.

Second Equation:

Let a body start its motion with velocity V_i. Let after time “ t “ its velocity becomes “ V_f “.

During such duration it covered a distance “ S “ with uniform acceleration “ a “.

We know that, distance covered by a body with average velocity is given as:

S = V_avt …………….(1)

Where V_av is the average velocity given as

V_av = V_i + V_f / 2 ………………(2)

Using first equation of motion:

V_{f =} V_i + at …………………. (3)

Substituting (3) in (2)

V_av = V_i + (V_i + at) / 2

V_av = 2V_i + at / 2

V_av = 2V_i / 2 + at / 2

V_av = V_i + ^½ at

Substituting (4) in (1)

S = (V_i + 1 / 2 at) t

S = V_it + ¹/₂ at²

Which is called second equation of motion.

Third Equation:

Let a body start its motion with a velocity “ V_i “ let after time “ t “ its velocity becomes “ V_f “.

During such duration its covered distance “S “ with uniform acceleration “ a “.

We know that distance covered by average velocity is given by:

S = V_av t ………(1)

Where V_av is the average velocity given as:

V_av = V_i + V_f / 2

OR

V_av = V_f + V_i / 2 …………. (2)

Using first equation of motion:

V_f = V_i + at

V_f = V_i = at

OR

t = V_f - V_i /a ……………..(3)

Substituting (2) and (3) in (1)

(1) becomes:

S = (V_f + V_i / 2) (V_f – V_i / a)

S = (V_f + V_i) (V_f – V_i) / 2a

2aS = (V_f + V_i ) (V_f - V_i) …………… (4)

Using relation:

(a + b) (a - b) = a² - b²

Here a = V_f b = V_i

(4) becomes:

2aS = V_f² - V_i²

Which is called 3^rd equation of motion.

Motion under Gravity : (Free Fall Motion)

“When body fall in such a way that no other force except the weight acting on it, then

such motion is called free fall motion and body is said to be free fall body.”

OR

“When body fall only because of gravitation attractive force of earth and except that

no other force acting in it than such motion is called motion is called motion under

gravity or free fall motion.”

If we drop a ball from certain height, if falls to the ground and its velocity increases

continuously till strickes the ground. Such acceleration is called acceleration due to

gravity. It is denoted by “ g “, it is taken positive when object moves upward. Its value in

different systems of units are as follows:

MKS System g = 9.8 m/s²

CGS System g = 980 cm/s²

FPS System g = 32 ft/s²